proportional weight paint deformation
Consider a Curve Deform modifier.





The curve modifier is applied to a long strip with high density as in the original question.  Plane scaled  into a strip.  Plane moved along the X axis in the example below.  The bone is not used in the images below.


Create a Spiral Curve manually or use the add on  Add Curve Extra Objects.
The dense vertex strip will be moved in the X direction to travel along the spiral.
Consider scaling in two dimensions the spiral. Scale Not Z axis.
The curve modifier is specified along the X axis in this example.  So scaling the strip along the X axis is easy and provides a movement.




Image above shows a shape key created with a proportional edit smooth from center of spiral

Lastly


Consider scaling the bone, not recommended, and a one minute experiment might be interesting.